New formulation of adiabatic theory of electron transfer in polar media

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Abstract
A new formalism is discussed for describing the process of an adiabatic outersphere electron transfer in a polar liquid within the framework of a continuum model of the medium. The generalized non-linear Maxwell equation for inertial polarization of the medium is suggested for describing the reaction dynamics. A characteristic equation is found, which defines the frequencies of the continuous medium in the presence of external charges, and its relation is established with respect to a conventional secular equation for the squares of the frequencies which appears in case the medium is simulated by a set of harmonic oscillators. With the object of accounting for fluctuations, a random force, calibrated according to the fluctuation-dissipation theorem, is introduced into the equation. If the potential energy of the system is defined by means of a two-level model, the resultant functional equation for polarization can be reduced to the generalized one-dimensional Langevin equation. For a medium with the Debye spectrum of dielectric permittivity ϵ(ω) an equation is obtained which agrees with the one known from other publications. A solution is found to the generalized Langevin equation for an arbitrary ϵ(ω) function. Reaction rate constants are calculated for various models of the medium. A comparison is made between the description of the rate constant within the framework of generalized transition state theory and the description by the generalized Langevin equation.